Problem: Solve for $x$ and $y$ using elimination. ${-x+2y = -8}$ ${x-3y = 7}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-x$ and $x$ cancel out. $-y = -1$ $\dfrac{-y}{{-1}} = \dfrac{-1}{{-1}}$ ${y = 1}$ Now that you know ${y = 1}$ , plug it back into $\thinspace {-x+2y = -8}\thinspace$ to find $x$ ${-x + 2}{(1)}{= -8}$ $-x+2 = -8$ $-x+2{-2} = -8{-2}$ $-x = -10$ $\dfrac{-x}{{-1}} = \dfrac{-10}{{-1}}$ ${x = 10}$ You can also plug ${y = 1}$ into $\thinspace {x-3y = 7}\thinspace$ and get the same answer for $x$ : ${x - 3}{(1)}{= 7}$ ${x = 10}$